A hollow cylinder of radius \(r\) is fixed with its axis horizontal. Points \(A\), \(B\), and \(O\) lie in the same vertical plane, with \(A\) and \(B\) on the smooth inner surface and \(O\) on the axis. The particle is projected vertically downwards from \(A\) with speed \(\sqrt{\frac32rg}\). It moves inside the cylinder and loses contact at \(B\).

(a) Find \(\alpha\).

(b) In the subsequent motion, find the greatest height above \(O\) reached by the particle, in terms of \(r\).